What is the intended way for players who do not own Beyond Light and/or Lightfall to complete these challenges and achieve the Top Challenger reward without the access to Strand and/or Stasis abilities?
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Stasis is F2P. As for Stranded Ritual - the Prismatic subclass counts if you have The Final Shape but besides that you're pretty much SOL as far as I know. Tangles may count if you have someone generate them but I haven't tested it. You aren't required to do all challenges, you need 42 but there are 47.